How Do You Solve Exponents Like X^3 + X^5 = 0?

[nightanole]

Well it appears that as i get higher in math, i lose the stuff i learned awhile ago. This type has me stumped for some reason.


x^3 + X^5=0 Or another one X^3 + x^4=0

I can break them down to X^3(1+X^2)=0 or X^3(X +1)=0

I just can seem to solve these simple guys.

 

[dav2008]

I'm not sure where you're having problems.

x³+x⁵=0
x³(1 + x²)=0
x³=0 or 1 + x²=0
x=0 (Assuming you only want real solutions)

 

[nightanole]

Hmm found something but can't explain the rule (help explaining please)

Got it to X^3(1+X)=0

for some reason you break it down to 2 solutions
x^3=0 and 1+x=0

since the first one doesn't work, the second one is the answer, which i can solve. X=-1

 

[dav2008]

Hmm found something but can't explain the rule (help explaining please)

Got it to X^3(1+X)=0

for some reason you break it down to 2 solutions
x^3=0 and 1+x=0

since the first one doesn't work, the second one is the answer, which i can solve. X=-1

The first one solves for x=0

 

[Zurtex]

If a*b=0 then it is obvious that either a=0, b=0 or a and b=0. So you need to look at both a being 0 or b being 0. This is why in general in maths we like things to equal 0 so we can solve them. For example a*b=1 doesn't tell us anything about a or b.

 

[nightanole]

Thanks guys, due to a brain fart this problem took me like 30min because i didnt factor, then i couldn't remember the zero thing till about 10min ago. I thought I am gona be a garbage man after this simple brain freeze. Last brain freeze was adding two digit number:)